Data commit

Task/Pells-equation/Swift/pells-equation.swift

@@ -0,0 +1,40 @@
+func solvePell<T: BinaryInteger>(n: T, _ a: inout T, _ b: inout T) {
+  func swap(_ a: inout T, _ b: inout T, mul by: T) {
+    (a, b) = (b, b * by + a)
+  }
+
+  let x = T(Double(n).squareRoot())
+  var y = x
+  var z = T(1)
+  var r = x << 1
+  var e1 = T(1)
+  var e2 = T(0)
+  var f1 = T(0)
+  var f2 = T(1)
+
+  while true {
+    y = r * z - y
+    z = (n - y * y) / z
+    r = (x + y) / z
+
+    swap(&e1, &e2, mul: r)
+    swap(&f1, &f2, mul: r)
+
+    (a, b) = (f2, e2)
+
+    swap(&b, &a, mul: x)
+
+    if a * a - n * b * b == 1 {
+      return
+    }
+  }
+}
+
+var x = BigInt(0)
+var y = BigInt(0)
+
+for n in [61, 109, 181, 277] {
+  solvePell(n: BigInt(n), &x, &y)
+
+  print("x\u{00b2} - \(n)y\u{00b2} = 1 for x = \(x) and y = \(y)")
+}